RE: Sly Cooper Playthrough

The only issue I'm trying to resolve at the moment are the black bars framing the screen during the stream.

In OBS, select the video source (either game capture, window capture or display capture), and try pressing Ctrl + F to 'Fit to Screen'. If your output aspect ratio is the same as your screen/game aspect ration it would have no black (empty) borders. Are you streaming at 1920x1080 (1080p) or 1280x720 (720p)?